Class groups of complex quadratic fields
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- by R. J. Schoof PDF
- Math. Comp. 41 (1983), 295-302 Request permission
Abstract:
We present 75 new examples of complex quadratic fields that have 5-rank of their class groups $\geqslant 3$. Only one of these fields has 5-rank of its class group $> 3$: The field ${\mathbf {Q}}(\sqrt { - 258559351511807} )$ has a class group isomorphic to \[ C(5) \times C(5) \times C(5) \times C(5) \times C(2) \times C(11828).\] The fields were obtained by applying ideas of J. F. Mestre to the 5-isogeny ${X_1}(11) \to {X_0}(11)$.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 41 (1983), 295-302
- MSC: Primary 12A25; Secondary 12-04, 12A50, 14K07
- DOI: https://doi.org/10.1090/S0025-5718-1983-0701640-0
- MathSciNet review: 701640